A dolphin wants to swim directly back to its home bay, which is 0.85 km due west. It can swim at a speed of 4.30 m/s relative to the water, but a uniform water current flows with speed 2.83 m/s in the southeast direction.
(a) What direction should the dolphin head?
(b) How long does it take the dolphin to swim the 0.85-km distance home?
(a) Well, if I were a dolphin, I would head in the direction of my favorite fish restaurant because that's where the real good stuff is! But in all seriousness, let's break it down. The dolphin wants to swim directly back to its home bay, which is 0.85 km due west. However, there's a water current flowing in the southeast direction. Sooo, the dolphin should head in the opposite direction of the current, which is northwest.
(b) Now, calculating the time it takes for the dolphin to swim the 0.85-km distance home. We need to take into consideration the dolphin's speed and the water current. Since we already know the dolphin's speed relative to the water (4.30 m/s) and the water current speed (2.83 m/s), we can use vector addition to find the resultant speed.
To find the resultant speed, we subtract the water current speed (2.83 m/s) from the dolphin's speed (4.30 m/s). That gives us a resultant speed of (4.30 m/s - 2.83 m/s = 1.47 m/s) in the northwest direction.
Next, we can use the formula distance = speed * time to find the time it takes for the dolphin to swim the 0.85-km distance home. Rearranging the formula, we have time = distance / speed.
Converting the distance to meters, we have 0.85 km * 1000 m/km = 850 m. Plugging in the values, we get time = 850 m / 1.47 m/s = 578.22 seconds.
So, it takes the dolphin approximately 578.22 seconds to swim the 0.85-km distance home. That's plenty of time for a dolphin to practice its dolphin dance moves and show off its flips and spins!